Finite Group Databasebeta

← C3×#73141 #11920919

Subgroups — C3×#73141 #11920919

Order 1152.

588 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×A4C211yesmaximal, characteristic
2C2×C3×A4⋊C8C212yesmaximal, complemented
3#73141C311yesmaximal, characteristic, direct product factor
4C3×#1779—31nomaximal
5C23×C3×A4C411yescharacteristic
6C2×C3×C4×A4—22no—
7C2×C3×C4×A4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9C3×A4⋊C8—22no—
10C3×#830—41nomaximal
11C24×C3×C4D311yescharacteristic
12C22×C4×A4—21no—
13C22×C4×A4C2×C311yescharacteristic
14C2×A4⋊C8C2×C312yescomplemented
15C2×C3×C22⋊C8—32no—
16C2×C3×C22⋊C8—31no—
17C2×C3×C22⋊C8—31no—
18C2×C3×C22⋊C8—32no—
19C22×C3×A4—21no—
20C22×C3×A4—21no—
21C22×C3×A4C812yescomplemented
22C22×C3×A4C2×C411yescharacteristic
23C22×C32×C4—41no—
24C3×C4×A4—21no—
25C3×C4×A4D412yes—
26C2×C3×C3⋊C8—42no—
27#1779—31noSylow
28C25×C3Dic311yescharacteristic
29C23×A4—21no—
30C23×A4C3×C411yescharacteristic
31C23×C3×C4—22no—
32C23×C3×C4—31no—
33C23×C3×C4—31no—
34C23×C3×C4—31no—
35C23×C3×C4—31no—
36C23×C3×C4—62no—
37C23×C3×C4Dic311yescharacteristic
38C23×C3×C4C2×D311yescharacteristic
39C2×C4×A4—24no—
40C2×C4×A4—22no—
41C2×C4×A4—21no—
42C2×C4×A4—21no—
43C2×C4×A4C3×C411yescharacteristic
44C2×C4×A4C22×C311yescharacteristic
45C22×C3×C8—32no—
46C22×C3×C8—32no—
47A4⋊C8—22no—
48C3×C22⋊C8—62no—
49C3×C22⋊C8—64no—
50C3×C22⋊C8—61no—
51C3×C22⋊C8—61no—
52C3×C22⋊C8—61no—
53C3×C22⋊C8—62no—
54C3×C22⋊C8—61no—
55#830—41no—
56C23×C32—41no—
57C2×C3×A4—22no—
58C2×C3×A4C22⋊C411yescharacteristic
59C2×C3×A4C2×C811yescharacteristic
60C2×C3×A4M1611yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4—82no—
64C3×C3⋊C8—82no—
65C24×C4C3×D311yescharacteristic
66C2×C22⋊C8—32no—
67C2×C22⋊C8—31no—
68C2×C22⋊C8—31no—
69C2×C22⋊C8—32no—
70C24×C3—21no—
71C24×C3—21no—
72C24×C3—31no—
73C24×C3—31no—
74C24×C3—32no—
75C24×C3—61no—
76C24×C3—61no—
77C24×C3C3⋊C812yescomplemented
78C24×C3C2×Dic311yescharacteristic
79C22×A4—22no—
80C22×A4—22no—
81C22×A4—21no—
82C22×A4—21no—
83C22×A4—22no—
84C22×A4—21no—
85C22×A4C3×C812yescomplemented
86C22×A4C2×C3×C411yescharacteristic
87C22×C3×C4—21no—
88C22×C3×C4—31no—
89C22×C3×C4—32no—
90C22×C3×C4—31no—
91C22×C3×C4—31no—
92C22×C3×C4—34no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—41no—
98C22×C3×C4—62no—
99C22×C3×C4—62no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102C22×C3×C4—62no—
103C22×C3×C4—62no—
104C22×C3×C4—62no—
105C22×C3×C4—62no—
106C22×C3×C4—62no—
107C22×C3×C4—81no—
108C22×C3×C4#6712yes—
109C22×C3×C4S411yescharacteristic
110C4×A4—22no—
111C4×A4—21no—
112C4×A4—22no—
113C4×A4C3×D412yes—
114C2×C3×C8—62no—
115C2×C3×C8—62no—
116C2×C3×C8—62no—
117C2×C3×C8—62no—
118C2×C3×C8—62no—
119C2×C3×C8—62no—
120C2×C3⋊C8—42no—
121C22×C32—42no—
122C22×C32—41no—
123C22×C32—81no—
124C22×C32—81no—
125C3×A4C22⋊C811yescharacteristic, complemented
126C32×C4—42no—
127C32×C4—81no—
128C25C3×Dic311yescharacteristic
129C23×C4—22no—
130C23×C4—31no—
131C23×C4—31no—
132C23×C4—31no—
133C23×C4—31no—
134C23×C4—62no—
135C23×C4C3×Dic311yescharacteristic
136C23×C4C2×C3×D311yescharacteristic
137C22×C8—32no—
138C22×C8—32no—
139C22⋊C8—62no—
140C22⋊C8—64no—
141C22⋊C8—61no—
142C22⋊C8—61no—
143C22⋊C8—61no—
144C22⋊C8—62no—
145C22⋊C8—61no—
146C23×C3—22no—
147C23×C3—31no—
148C23×C3—31no—
149C23×C3—32no—
150C23×C3—31no—
151C23×C3—31no—
152C23×C3—32no—
153C23×C3—32no—
154C23×C3—32no—
155C23×C3—32no—
156C23×C3—31no—
157C23×C3—41no—
158C23×C3—61no—
159C23×C3—61no—
160C23×C3—61no—
161C23×C3—61no—
162C23×C3—62no—
163C23×C3—61no—
164C23×C3—61no—
165C23×C3—62no—
166C23×C3—62no—
167C23×C3—61no—
168C23×C3—64no—
169C23×C3—81no—
170C23×C3C2×C3⋊C811yescharacteristic
171C23×C3#20811yescharacteristic
172C23×C3#21711yescharacteristic
173C23×C3SL(2,ℤ/4)11yescharacteristic
174C2×A4—24no—
175C2×A4—22no—
176C2×A4—21no—
177C2×A4—21no—
178C2×A4—21no—
179C2×A4C3×C22⋊C411yescharacteristic
180C2×A4C2×C3×C811yescharacteristic
181C2×A4C3×M1611yescharacteristic
182C2×C3×C4—22no—
183C2×C3×C4—31no—
184C2×C3×C4—32no—
185C2×C3×C4—32no—
186C2×C3×C4—32no—
187C2×C3×C4—32no—
188C2×C3×C4—31no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—62no—
192C2×C3×C4—61no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195C2×C3×C4—62no—
196C2×C3×C4—64no—
197C2×C3×C4—62no—
198C2×C3×C4—61no—
199C2×C3×C4—82no—
200C2×C3×C4—84no—
201C2×C3×C4—81no—
202C2×C3×C4—81no—
203C2×C3×C4SL(2,ℤ/4)11yescharacteristic
204C2×C3×C4C2×S411yescharacteristic
205C3×C8—122no—
206C3×C8—122no—
207C3⋊C8—82no—
208C2×C32—41no—
209C2×C32—41no—
210C2×C32—41no—
211C2×C32—82no—
212C24—21no—
213C24—21no—
214C24—31no—
215C24—31no—
216C24—32no—
217C24—61no—
218C24—61no—
219C24C3×C3⋊C812yescomplemented
220C24C2×C3×Dic311yescharacteristic
221C22×C4—21no—
222C22×C4—31no—
223C22×C4—32no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—34no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—61no—
234C22×C4—61no—
235C22×C4—62no—
236C22×C4—62no—
237C22×C4—62no—
238C22×C4—62no—
239C22×C4—62no—
240C22×C4C3×#6712yes—
241C22×C4C3×S411yescharacteristic
242C2×C8—62no—
243C2×C8—62no—
244C2×C8—62no—
245C2×C8—62no—
246C2×C8—62no—
247C2×C8—62no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—31no—
251C22×C3—31no—
252C22×C3—31no—
253C22×C3—31no—
254C22×C3—31no—
255C22×C3—31no—
256C22×C3—31no—
257C22×C3—31no—
258C22×C3—31no—
259C22×C3—34no—
260C22×C3—32no—
261C22×C3—41no—
262C22×C3—42no—
263C22×C3—62no—
264C22×C3—62no—
265C22×C3—62no—
266C22×C3—62no—
267C22×C3—61no—
268C22×C3—62no—
269C22×C3—62no—
270C22×C3—62no—
271C22×C3—61no—
272C22×C3—61no—
273C22×C3—81no—
274C22×C3—81no—
275C22×C3—82no—
276C22×C3—82no—
277C22×C3—81no—
278C22×C3—82no—
279C22×C3#83011yescharacteristic, complemented
280C22×C3A4⋊C812yescomplemented
281C22×C3C2×SL(2,ℤ/4)11yescharacteristic
282A4—21no—
283A4C3×C22⋊C811yescharacteristic, complemented
284C3×C4—21no—
285C3×C4—32no—
286C3×C4—42no—
287C3×C4—61no—
288C3×C4—81no—
289C3×C4—82no—
290C3×C4—82no—
291C3×C4GL(2,ℤ/4)12yes—
292C32—41noSylow
293C23—22no—
294C23—31no—
295C23—31no—
296C23—32no—
297C23—31no—
298C23—31no—
299C23—32no—
300C23—32no—
301C23—31no—
302C23—32no—
303C23—32no—
304C23—61no—
305C23—61no—
306C23—61no—
307C23—61no—
308C23—62no—
309C23—61no—
310C23—61no—
311C23—62no—
312C23—62no—
313C23—61no—
314C23—64no—
315C23C2×C3×C3⋊C811yescharacteristic
316C23C3×#20811yescharacteristic
317C23C3×#21711yescharacteristic
318C23C3×SL(2,ℤ/4)11yescharacteristic
319C2×C4—22no—
320C2×C4—31no—
321C2×C4—32no—
322C2×C4—32no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—31no—
326C2×C4—62no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—62no—
331C2×C4—64no—
332C2×C4—62no—
333C2×C4—61no—
334C2×C4C3×SL(2,ℤ/4)11yescharacteristic
335C2×C4C2×C3×S411yescharacteristic
336C8—122no—
337C8—122no—
338C2×C3—22no—
339C2×C3—31no—
340C2×C3—31no—
341C2×C3—31no—
342C2×C3—31no—
343C2×C3—41no—
344C2×C3—41no—
345C2×C3—41no—
346C2×C3—62no—
347C2×C3—82no—
348C2×C3—84no—
349C2×C3—81no—
350C2×C3—81no—
351C2×C3—81no—
352C2×C3C2×A4⋊C811yescharacteristic
353C2×C3#540911yescharacteristic
354C2×C3#543211yescharacteristic
355C22—21no—
356C22—21no—
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—31no—
366C22—34no—
367C22—32no—
368C22—62no—
369C22—62no—
370C22—62no—
371C22—62no—
372C22—61no—
373C22—62no—
374C22—62no—
375C22—62no—
376C22—61no—
377C22—61no—
378C22C3×#83011yescharacteristic, complemented
379C22C3×A4⋊C812yescomplemented
380C22C2×C3×SL(2,ℤ/4)11yescharacteristic
381C4—21no—
382C4—32no—
383C4—61no—
384C4C3×GL(2,ℤ/4)12yes—
385C3—41no—
386C3—81no—
387C3#7314111yescharacteristic, direct product factor
388C2—22no—
389C2—31no—
390C2—31no—
391C2—31no—
392C2—31no—
393C2—62no—
394C2C2×C3×A4⋊C811yescharacteristic
395C2C3×#540911yescharacteristic
396C2C3×#543211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×S4
commutatorC2×A4C2×C3×C8
FrattiniC2×C4C2×C3×S4
FittingC24×C3×C4D3
socleC24×C3C2×Dic3
prime radicalC23×C3×A4C4
cosocleC2×C4×A4C22×C3
hypercenterC22×C3×C4S4
hypocenterA4C3×C22⋊C8
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×A4⋊C8C2semidirect
3. #73141C3direct (N × H)
14. C2×A4⋊C8C2×C3semidirect
21. C22×C3×A4C8semidirect
77. C24×C3C3⋊C8semidirect
85. C22×A4C3×C8semidirect
125. C3×A4C22⋊C8semidirect
219. C24C3×C3⋊C8semidirect
279. C22×C3#830semidirect
280. C22×C3A4⋊C8semidirect
283. A4C3×C22⋊C8semidirect
378. C22C3×#830semidirect
379. C22C3×A4⋊C8semidirect
387. C3#73141direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C4×A42
C2×C3×A4⋊C82
#731413
C3×#17793
C3×#8304